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Dipartimento di Economia "Marco Biagi"
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Dipartimento Educazione e Scienze Umane

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2007 - Correlated-gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. II. Coupled cluster and density-functional theory results for eight small molecules [Articolo su rivista]

The quantum mechanical current density induced in a molecule by an external magnetic field isinvariant to translations of the coordinate system. This fundamental symmetry is exploited toformally annihilate the diamagnetic contribution to the current density via the approach of“continuous transformation of the origin of the current density-diamagnetic zero” CTOCD-DZ.The relationships obtained by this method for the magnetic shielding at the nuclei are intrinsicallyindependent of the origin of the coordinate system for any approximate computational schemerelying on the algebraic approximation. The authors report for the first time an extended series oforigin-independent estimates of nuclear magnetic shielding constants using the CTOCD-DZapproach at the level of density functional theory DFT with four different types of functionals andunrelaxed coupled cluster singles and doubles linear response CCSD-LR theory. The resultsobtained indicate that in the case of DFT the procedure employed is competitive with currentlyadopted computational methods allowing for basis sets of gauge-including atomic orbitals, whereaslarger differences between CTOCD-DZ and common origin CCSD-LR results are observed due tothe incomplete fulfillment of hypervirial relations in standard CCSD-LR theory. It was foundfurthermore that the unrelaxed CCSD-LR calculations predict larger correlation corrections for theshielding constants of almost all nonhydrogen atoms in their set of molecules than the usual relaxedenergy derivative CCSD calculations. Finally the results confirm the excellent performance of Kealand Tozer’s third functional, in particular, for the multiply bonded systems with a lot of electroncorrelation, but find also that the simple local density functional gives even better results for the fewsingly bonded molecules in their study where correlation effects are small.

2005 - Ring current effects on nuclear magnetic shielding of carbon in the benzene molecule [Articolo su rivista]
Mb, Ferraro; Faglioni, Francesco; Ligabue, Andrea; S., Pelloni; Lazzeretti, Paolo

The differential Biot-Savart law of classical electrodynamics was applied to develop a ring current model for the magnetic shielding of the carbon nucleus in benzene. It is shown that the local effect of the pi currents, induced by a magnetic field normal to the molecular plane, on the sigma(C) out-of-plane shielding tensor component vanishes. However, approximately 10% of sigma(C) is due to the shielding contributions from pi current density in the region of the other carbon atoms. Magnetic shielding density maps obtained via quantum mechanical procedures confirm the predictions of the classical model.

2005 - The ring-current model of the paratropic pentalene molecule [Articolo su rivista]
Ig, Cuesta; Ligabue, Andrea; AS de, Meras; Lazzeretti, Paolo

The ring-current model for the pentalene molecule has been constructed by ab initio techniques. The current density vector field has been used to obtain magnetic shielding density maps for the different protons. It is shown that the paramagnetic flow of the pi electrons causes an increase of the out-plane component of proton shielding tensors, that is overall shielding. Distant portions of the it flow also shield carbon nuclei.

2004 - Molecular response to a time-independent non-uniform magnetic-field [Articolo su rivista]
Faglioni, Francesco; Ligabue, Andrea; S., Pelloni; A., Soncini; Lazzeretti, Paolo

The response of a molecule to a static inhomogeneous magnetic-field is rationalized via multipole magnetic susceptibilities and induced magnetic multipole and anapole moments. The energy of the molecule interacting with the external field is expressed as a Taylor series in the powers of the field and its gradient at the origin of the coordinate system. It involves magnetic multipole tensors of increasing rank, which can be evaluated via quantum mechanical approaches. An electronic energy shift is caused by the feedback interaction between the induced magnetic dipole moment and the external magnetic field, and between the induced magnetic quadrupole moment and the gradient of the magnetic field. It is shown that, for a static magnetic field with uniform gradient, the magnetic quadrupole moment is origin-dependent, but the total interaction energy and the induced magnetic dipole are invariant to a translation of the coordinate system. The formal advantages of a Geertsen approach to third- and fourth-rank mixed-multipole susceptibilities are discussed.

2004 - Ring-current models from the differential Biot-Savart law [Articolo su rivista]
S., Pelloni; Ligabue, Andrea; Lazzeretti, Paolo

The differential Biot-Savart law provides simple models for the pi ring currents induced in diatropic and paratropic planar conjugated molecules by a perpendicular magnetic field. The model predictions are confirmed by ab initio maps of nuclear magnetic shielding density. The effects on the protons and on the ring carbon atoms from the closest and furthest segments of the current loop are easily interpreted.

2003 - Correlated and gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach [Articolo su rivista]
Ligabue, Andrea; Spa, Sauer; Lazzeretti, Paolo

We report for the first time an extended series of correlated origin independent calculations of nuclear magnetic shielding tensors using the approach of continuous transformation of the origin of the current density to annihilate its diamagnetic contribution. A systematic study was undertaken to develop optimal basis sets for H, C, N, O, F correlated nuclear magnetic shieldings, looking for the best compromise between accuracy and size. Beyond Hartree-Fock calculations were carried out at two levels of accuracy, the multiconfigurational self-consistent field based on the complete active space scheme, and the second-order polarization propagator approximation (SOPPA). In addition we present the first shielding calculations employing the second-order polarization propagator approximation with coupled cluster singles and doubles amplitudes SOPPA (CCSD).

2003 - Magnetic response of dithiin molecules: is there anti-aromaticity in nature? [Articolo su rivista]
S., Pelloni; Faglioni, Francesco; A., Soncini; Ligabue, Andrea; Lazzeretti, Paolo

Ab initio current density formalism is used to investigate the response to external magnetic fields of the only knownnaturally occurring moieties which are formally anti-aromatic, i.e., dithiines. Magnetic susceptibility, nuclear shieldingconstants, and the topology of induced current densities indicate that although these molecules satisfy H€uckels rule forbeing anti-aromatic, they are not. In chiral dithiines, the multipolar expansion of the response contains non-vanishinganapole terms associated with spinning cuff current lines.

2003 - Theoretical determination of the magnetic properties of 2-pyrone and 4-pyrone, and o-benzoquinone and p-benzoquinone [Articolo su rivista]
Ligabue, Andrea; Lazzeretti, Paolo

A series of theoretical procedures, relying on the conventional common-origin and distributed-origin approaches, and adopting extended gaugeless as well as London basis sets, have been applied at the Hartree-Fock level of accuracy to predict magnetic susceptibilities and nuclear magnetic shieldings of four molecular systems that aroused particular interest and discussion concerning their aromatic character. The theoretical results are of near Hartree-Fock quality. Comparison with experimental values for magnetic susceptibilities seems to indicate that the latter need to be revised. Analysis of calculated properties and of plots of current density induced by the magnetic field in the pi-electrons provides simple and effective tools for the classification of 2- and 4-pyrones, and o- and p-benzoquinone as non-aromatic.

2002 - An efficient coupled Hartree-Fock computational scheme for parity-violating energy differences in enantiomeric molecules [Articolo su rivista]
M., Gnani; Lazzeretti, Paolo; Ligabue, Andrea; U., Pincelli; A., Soncini

A coupled Hartree-Fock scheme for fast computation of parity-violating energy differences in big-size chiral molecules of biological interest has been developed within the McWeeny-Diercksen density matrix formulation. All the required integral files and relevant matrices are represented over a basis set of atomic spin orbitals, avoiding transformation to the molecular basis. Two-electron spin-orbit matrix elements need not to be stored within the computer code implementing the theoretical method. (C) 2002 Elsevier Science B.V. All rights reserved.

2002 - On the resolution of the optical rotatory power of chiral molecules into atomic terms. A study of hydrogen peroxide [Articolo su rivista]
Ligabue, Andrea; Lazzeretti, Paolo; Mpb, Varela; Mb, Ferraro

An additive scheme for resolving average optical rotatory power of a molecule into atomic contributions, based on the acceleration gauge for the electric dipole, and/or the torque formalism, has been applied to hydrogen peroxide. Extended calculations have been carried out to test the reliability of the partition method. Gross atomic isotropic contributions to the average molecular property from oxygen and hydrogen atoms have been evaluated. The force and torque gauges provide different numerical values for atomic contributions.

2002 - Ring currents and magnetic properties of s-indacene, an archetypal paratropic, non-antiaromatic molecule [Articolo su rivista]
R., SORIANO JARTIN; Ligabue, Andrea; A., Soncini; Lazzeretti, Paolo

Magnetic susceptibility and nuclear magnetic shielding at the nuclei of s-indacene have been evaluated by a series of different approximations and a large Gaussian basis set. An ab initio model of magnetic field induced current density was developed, showing that intense paramagnetic flow takes place within the, electrons. It causes strong upfield chemical shift of protons attached to hexagonal and pentagonal rings. The magnetic susceptibility tensor is typical of a diamagnetic molecule but is characterized by small anisotropy. Group-theoretical methods developed by Steiner and Fowler indicate that s-indacene can be classified as a 2p + 4d system, in which the paramagnetic circulation of two electrons in the highest occupied orbital of B-g symmetry overwhelms the diamagnetic flow of four electrons in occupied A. orbitals. Because of its unique structural and magnetic properties, s-indacene can be described as a limit system between the classes of aromatic and antiaromatic molecules.

2002 - The Leap-frog Effect of Ring Currents in Benzene [Articolo su rivista]
Ligabue, Andrea; A., Soncini; Lazzeretti, Paolo

Symmetry arguments show that the ring-current model proposed by Pauling, Lonsdale, andLondon to explain the enhanced diamagnetism of benzene is flawed by an intrinsic drawback. The minimalbasis set of six atomic 2p orbitals taken into account to develop such a model is inherently insufficient topredict a paramagnetic contribution to the perpendicular component of magnetic susceptibility in planarring systems such as benzene. Analogous considerations can be made for the hypothetical H6 cyclicmolecule. A model allowing for extended basis sets is necessary to rationalize the magnetism of aromatics.According to high-quality coupled Hartree-Fock calculations, the trajectories of the current density vectorfield induced by a magnetic field perpendicular to the skeletal plane of benzene in the ð electrons arenoticeably different from those typical of a Larmor diamagnetic circulation, in that (i) significant deformationof the orbits from circular to hexagonal symmetry occurs, which is responsible for a paramagnetic contributionof ð electrons to the out-of-plane component of susceptibility, and (ii) a sizable component of the ð currentdensity vector parallel to the inducing field is predicted. This causes a waving motion of ð electrons;streamlines are characterized by a “leap-frog effect”.

2002 - Theoretical determination of magnetic properties of planar benzene isomers [Articolo su rivista]
Ligabue, Andrea; Lazzeretti, Paolo

Four theoretical methods, using continuous transformation of the origin of the current density (CTOCD) to annihilate either the diamagnetic or the paramagnetic contribution, have been employed at the coupled Hartree-Fock level of accuracy to evaluate magnetic susceptibility and nuclear magnetic shielding of five planar molecules with the chemical formula C6H6. The results have been compared with corresponding estimates from basis sets of London orbitals, showing the near Hartree-Fock quality of calculated values and the practicality of CTOCD approaches. Maps of streamlines and intensity of the current density induced in the pi -electrons by a stationary magnetic- field perpendicular to the molecular plane are shown to interpret the different magnetic response properties of benzene isomers by means of the Ring-Current model. The plots show delocalized flow in benzene, determining its enhanced diamagnetism. Diamagnetic loops, localized in the region of carbon-carbon bonds, and a paramagnetic vortex in the vicinity of electronic centroid, are found in 3,4-dimethylenecyclobutene and trimethylenecyclopropane. This pattern is typical of conjugated nonaromatic molecules. Delocalized diamagnetic circulation observed in fulvene explains its exalted magnetic susceptibility.

2000 - Parity-violating effects in asymmetric chemical reactions: A theoretical study on the CHFClBr molecule [Articolo su rivista]
Soncini, A.; Ligabue, A.; Lazzeretti, Paolo; Zanasi, Riccardo

A coupled Hartree-Fock procedure has been employed to estimate the parity-violating energy contribution due to electroweak interaction in the vicinity of the transition point of a chemical reaction path starting from achiral reagents and producing the chiral CHFClBr molecule. The calculations demonstrate that (i) the S enantiomer is a reaction product more stable than its minor image by approximate to1 X 10(-17) hartree; (ii) in the transition state of the reaction, the chiral activated complex evolving toward the S-CHFClBr species is more stable, by approximate to2.3 X 10(-17) hartree, than the enantiomeric activated complex that would yield the R-CHFClBr species. These results suggest that kinetic effects at work during chemical syntheses of chiral molecules might be more significant than the different thermodynamical stability of the mio mirror-image reaction products in determining the final; configuration and to explain homochirality.

2000 - Theoretical Determination of Parity-Violating Vibrational Frequency Differences between the Enantiomers of the CHFClBr Molecule [Articolo su rivista]
R. G., Viglione; R., Zanasi; Lazzeretti, Paolo; Ligabue, Andrea

A coupled Hartree-Fock procedure has been employed to estimate the frequency shift in the infrared spectraof the S and R enantiomers of the CHFClBr molecule due to the parity-violating electroweak interaction. Thecalculations indicate that a resolving power n /Dn'131016, i.e., three orders of magnitude larger than thatobtained in recent experiments, would be necessary to detect the parity-violating effects. The largest frequencyshift was found for C-Cl stretching.

1999 - Current density maps, magnetizability and nuclear magnetic shielding tensors for anthracene, phenanthrene and triphenylene [Articolo su rivista]
Ligabue, Andrea; U., Pincelli; Lazzeretti, Paolo; R., Zanasi

Ab initio magnetically induced ð-electron (first-order) current density maps and second-order magneticproperties, i.e., magnetizabilies, proton, and 13 C magnetic shielding tensors, calculated at coupled Hartree-Fock level of theory by means of the continuous transformation of origin of the current density method (CTOCD),are presented for a series of polycyclic aromatic hydrocarbons. The reliability of the current density maps isdocumented by the nice agreement between theoretical values for principal values of magnetizabilities andproton magnetic shieldings and corresponding experimental data presently available. For all three of themolecules, the ð-electron current flows mainly on the external circuit of carbon atoms. Other intense circulationslocalized on a single ring take place over the central hexagon of anthracene and, on the contrary, on theexternal hexagons of phenanthrene and triphenylene. In light of the results obtained in the present work, e.g.,taking advantage of high quality current density maps, important details of the ring current model for themolecules under study can be reexamined. Eventually, it is shown that the fundamental information which canbe gained from knowledge of the principal components of the magnetic response tensors is easily accessibleby means of the CTOCD computational method adopted here.

1999 - On the stabilization of natural L-alpha-amino acids and D-sugars via parity-violating effects. [Capitolo/Saggio]
Lazzeretti, Paolo; Ligabue, Andrea; A., Soncini; R., Zanasi

Classically a chiral molecule and its enantiomer have been considered energetically equivalent:<ΨDHpcΨD>=<ΨLP−1HpcPΨL>=<ΨLHpcΨL>as the parity-conserving hamiltonian Hpc does not change under the transformation P−1 HpcP, where P is the parity operator which transforms the wavefunction of one enantiomer into the other. However the parity-violating weak interactions ensure that this equivalence is no longer exact.

1999 - Theoretical results which strengthen the hypothesis of electroweak bioenantioselection [Articolo su rivista]
R., Zanasi; Lazzeretti, Paolo; Ligabue, Andrea; A., Soncini

It is shown via a large series of numerical tests on two fundamental organic molecules, the L-a-amino acidL-valine and the sugar precursor hydrated D-glyceraldheyde, that the ab initio calculation of the parityviolatingenergy shift, at the random-phase approximation level of accuracy, provides results that are about oneorder of magnitude larger than those obtained by means of less accurate methods employed previously. Thesefindings would make more plausible the hypothesis of electroweak selection of natural enantiomers via theKondepudi-Nelson scenario, or could imply that Salam phase-transition temperature is higher than previouslyinferred: accordingly, the hypothesis of terrestrial origin of life would become more realistic.